## _wp1449

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### Introduction and key empirical observations
- Sovereign debt perceived as riskier in developing than developed countries, with exceptions (recent European debt crisis).
- 2012 examples: Belgium, United Kingdom, and the United States have net government debt-to-GDP ratios exceeding 0.8 and sovereign ratings at or above AA; Argentina and Ecuador have gross debt-to-GDP ratios at 0.48 and 0.22, respectively, but ratings of B and B− (Standard & Poor’s (2013)).
- Fiscal limits are defined as the maximum debt level a government is able and willing to service; fiscal limits are generally lower in developing countries.
- Paper uses a DSGE model with sovereign default risks to:
  - Simulate fiscal limit distributions (illustrated for Argentina).
  - Analyze fiscal policy effects under different government indebtedness states.
- Fiscal limits in the model are uncertain and forward-looking; default depends on whether current debt exceeds a realized effective fiscal limit drawn from a distribution based on economic fundamentals.
- Sovereign risk premia arise endogenously and nonlinearly as a function of government indebtedness.

### Main empirical drivers of lower fiscal limits
- Revenue collection capacity:
  - Effective tax collection (maximum effective tax rate) and political risk are key determinants of fiscal limits.
  - Callen et al. (2003) estimate effective tax rate for emerging markets outside eastern Europe is only 10 percent, compared with industrial countries’ average above 30 percent.
- Real exchange rate fluctuations:
  - Increase dispersion of fiscal limit distributions via balance-sheet effects when external borrowing is substantial.
  - Currency mismatch (revenues in local currency vs. foreign-currency liabilities) raises default risk for a given debt size.
- Other noted factors (discussed in literature but not modeled here): debt intolerance, credibility, and default history.

### Model overview
- Economy: small open, real economy with two production sectors: nontradables (N) and tradables (T).
- Shocks included: total factor productivity (TFP), spending and tax policy, and terms of trade.
- Solution methods:
  - Nonlinear model solved by the monotone mapping method for simulations.
  - Linearized model (assuming no sovereign default) fitted to Argentina’s post-default data (early 2000s) to estimate shock processes.

### Households and firms (structure and key equations)
- Household utility and consumption aggregator:
  - Effective consumption: ̃c_t = [ω(c_t)^{(ν−1)/ν} + (1−ω)(g_t)^{(ν−1)/ν}]^{ν/(ν−1)}
  - Lifetime utility: U_t = Σ_{t=0}^∞ β^t [log ̃c_t − φ l_t^{1+σ}/(1+σ)]
  - Parameters: ω, ν, β ∈ (0,1), σ inverse of Frisch elasticity.
- Production and TFP:
  - y^j_t = a^j_t (k^j_{t−1})^{1−α_j} (l^j_t)^{α_j}, j ∈ {N, T}
  - ln(a^j_t / a^j) = ρ_a ln(a^j_{t−1} / a^j) + ε^a_t, ε^a_t ∼ N(0, σ_a^2)
- Tradable sector: produces only for exports; domestic tradable demand met by imports priced at s_t.
- Terms of trade ξ_t ≡ p^x_t s_t follow:
  - ln(ξ_t / ξ) = ρ_ξ ln(ξ_{t−1} / ξ) + ε^ξ_t, ε^ξ_t ∼ N(0, σ_ξ^2)

### Government: budget, bonds, and default
- Government issues external bond b*_t, collects income tax τ_t, finances government consumption g_t, transfers z, and debt service.
- Period flow budget constraint:
  - T_t + q_t s_t b*_t = s_t (1−∆_t) b*_{t−1} + p^G_t g_t + z
  - T_t ≡ τ_t (w_t l_t + r^N_t k^N_{t−1} + r^T_t k^T_{t−1}), q_t = β E_t (1 − ∆_{t+1})
- Default scheme:
  - ∆_t = 0 if b*_{t−1} < B^{max}_t; ∆_t = d if b*_{t−1} ≥ B^{max}_t
  - B^{max}_t ∼ B^{max}(S_t), where S_t is the state vector (see simulation procedure).

### Fiscal rules and behavioral assumptions
- Government consumption responds procyclically with a one-quarter delay to output y_{t−1}.
- Tax and government consumption rules:
  - ln(τ_t / τ) = ρ_τ ln(τ_{t−1} / τ) + γ ln(b^{d*}_t / b^*) + ε^τ_t, γ > 0
  - ln(g_t / g) = ρ_g ln(g_{t−1} / g) + η_g ln(y_{t−1} / y) + ε^g_t
  - ε^τ_t, ε^g_t ∼ N(0, σ_i^2), i ∈ {τ, g}
- In the model, income taxes are the adjustment instrument to maintain debt sustainability; government consumption is assumed harder to cut in developing-country contexts.

### Aggregation and market clearing
- Aggregate output in local goods:
  - y_t = p^N_t y^N_t + ξ_t s_t y^T_t
- Balance-of-payments condition:
  - c_t + i_t + investment adjustment cost terms + p^G_t g_t − y_t = s_t [ q_t b*_t − (1 − ∆_t) b*_{t−1} ]

### Parameter calibration and estimation (exact values)
- Calibration highlights:
  - β = 0.98
  - δ = 0.03
  - Tradable share in CPI for Argentina = 0.53
  - φ_G = 0.6
  - ω = 0.8
  - ν = 0.49
  - χ = 0.44
  - ξ_l = 1
  - κ = 1.7
  - Labor shares: α_N = 0.6; α_T = 0.55
  - φ (utility weight on leisure) set so steady-state labor = 0.2 (calibrated later as 40.6 in parameter list)
  - Steady-state fiscal calibration (sample 2003Q1:2012Q2):
    - Government spending share of output = 0.1476
    - Tax rate (total revenues to GDP) = 0.227
    - Debt-to-annual output ratio (external public debt) = 0.24
- Default and haircut calibration:
  - Constant quarterly haircut rate: 0.07 (equivalent to 0.28 for the annual rate)
- Estimation priors and posteriors:
  - Priors: AR(1) ρ’s mean 0.5 (sd 0.2); σ’s inverse gamma mean 0.1; η_g prior mean 0.5 (sd 0.2); γ prior mean 0.05 (sd 0.02), γ > 0.
  - Posterior-mode estimates: η_g = 0.1; γ = 0.06.
- Full parameter list (exact numeric entries):
  - β 0.98
  - σ 2
  - δ 0.03
  - χ 0.44
  - χ_l 1
  - φ 0.47
  - φ_l 0.5019
  - φ_g 0.6
  - φ (utility weight on leisure) 40.6
  - α_N 0.6
  - α_T 0.55
  - κ 1.7
  - ω 0.8
  - ν 0.49
  - τ 0.227
  - d 0.07
  - η_g 0.10
  - γ_τ_t 0.06
  - ρ_g 0.37
  - ρ_τ 0.77
  - ρ_a 0.82
  - ρ_ξ 0.76
  - σ_g 2.32
  - σ_τ 9.11
  - σ_a 1.48
  - σ_ξ 2.87

### Fiscal limit definition and simulation methodology
- Fiscal limit definition:
  - Maximum level of debt in units of local goods that a government is able and willing to service.
  - Period maximum primary surplus computed under τ_t = τ_max.
  - Political willingness proxied by θ ∈ (0,1]; fiscal limit equals discounted sum of future maximum primary surpluses multiplied by θ.
- Baseline parameterization for fiscal limit simulations:
  - Baseline τ_max = 0.29.
  - Argentina average ICRG political risk rating = 66.5 out of 100 → θ set to 0.67 for Argentina.
- State-dependent fiscal limit expression:
  - B_max(S_i) ∼ [ sum_{i=0}^∞ β^t θ 1_{smax_{t+i}} (T^max_{t+i} − p^G_{t+i} g_{t+i} − z) ] where superscript max indicates variables under τ_t = τ_max and S_t = {ε^a_t, ε^g_t, ε^ξ_t, k^N_{t−1}, k^T_{t−1}}.
- Monte Carlo simulation procedure for fiscal limit distributions:
  - For each simulation j:
    - Draw exogenous shocks ε^{a,j}_{t+i}, ε^{g,j}_{t+i}, ε^{ξ,j}_{t+i} for i = 1, ...,1000 conditional on starting state S_t.
    - Obtain T^{max,j}_{t+i} and s^{max,j}_{t+i} via interpolating decision rules m_T(.) and m_s(.).
    - Compute B^{max,j}(S_t) = ∑_{i=0}^∞ β^i θ^{1 / s^{max,j}_{t+i}} (T^{max,j}_{t+i} − p^G_{j,t+i} g_{j,t+i} − z). (equation III.7)
  - Repeat for 10,000 simulations (j = 1, ...,10000) to obtain distribution {B^{max,j}(S_t)}_{j=1}^{10000}.
- Nonlinear decision-rule solution steps (convergence tolerance exactly 1e−7) summarized:
  - Discretize state space, initialize decision rules (m_p0, m_l0, m_k0), iterate solving nonlinear model at each grid point with τ = τ_max to update rules until convergence; then compute m_T(.) and m_s(.), and proceed to MCMC simulation.
  - When solving model allowing defaults, state space S_t = {b^{d*}_t, ε^a_t, ε^g_t, k^N_{t−1}, k^T_{t−1}} and analogous iteration on rules f_b, f_p, f_l, f_k with same tolerance 1e−7.

### Baseline fiscal limit distribution and historical comparisons (Argentina)
- Baseline CDF properties:
  - Default probability is roughly zero when the debt-to-GDP ratio is below 0.45.
  - Default probability climbs to almost 1 when the debt-to-GDP ratio reaches 0.7.
- Historical external debt-to-GNP ratios at years of default:
  - 0.55 in 1982.
  - 0.53 in 2001.
- The estimated fiscal limits for Argentina cover actual debt levels in the two recent sovereign default episodes.

### Sensitivity to revenue capacity and political risk (exact comparative statistics)
- Baseline and alternatives:
  - Baseline: τ_max = 0.29, θ = 0.67 (solid line).
  - Alternative A: τ_max = 0.35, θ = 0.67 (dashed-solid line).
  - Alternative B: τ_max = 0.35, θ = 0.8 (dashed line).
- Impacts on mean of fiscal limit distribution (means reported exactly):
  - Baseline mean: 0.61.
  - τ_max = 0.35, θ = 0.67 → mean = 1.02.
  - τ_max = 0.35, θ = 0.8 → mean = 1.22.
- Quantitative sensitivity:
  - A one-percentage point increase in the tax rate raises the mean of fiscal limits by almost 7 percent of GDP for Argentina.
- Policy insight:
  - Strengthening revenue collection (raising τ_max) can be effective in raising fiscal limits in developing countries; cutting government spending offers limited room given low government spending shares.

### Terms-of-trade volatility and devaluation experiments (exact results)
- Terms-of-trade volatility experiment:
  - Baseline σ_ξ = 2.87.
  - Alternative (twice volatility) σ_ξ = 5.74.
  - At debt-to-GDP ratio 0.55, default probability rises from 0.06 (baseline) to 0.25 (higher σ_ξ).
- Large devaluation experiment:
  - Subject economy to a −30-percent terms-of-trade shock → initial real depreciation of 20 percent from steady state.
  - At debt-to-GDP ratio 0.55, default probability increases from 0.06 (baseline) to about 0.4 (conditional).
- Implication:
  - Large negative terms-of-trade shocks or sudden real depreciations can substantially shift fiscal limit distributions left and raise default probabilities; other shocks (e.g., capital flow shocks) can similarly affect fiscal limits.

### Fiscal policy in a highly indebted economy — calibration to Argentina (experiments and findings)
A. High-debt state construction and initial impacts
- High-debt scenario:
  - Sequence of small negative TFP shocks of −1percent each period for 57 quarters starting in the steady state (t = −80).
  - Initial steady-state debt-to-annual GDP ratio = 0.24.
  - At t = 0, debt-to-annual GDP ratio climbs to 0.52.
  - From t = −80 to −1, government sets γ = 0.04 (below estimated γ = 0.06).
  - At t = 0, k^N_{−1} and k^T_{−1} are about 14 and 9 percent below their steady-state values.
  - At t = 0 the interest rate increases by about 43 basis points relative to the steady-state level.
- Short-run macro impacts at t = 0 (relative to steady state):
  - Consumption: falls by 8.0 percent.
  - Investment/saving: falls by 5.6 percent.
  - Labor: increases by 1.4 percent.
  - Output: falls by 4.3 percent.

B. Fiscal consolidation scenarios and trade-offs (exact scenarios and outcomes)
- Consolidation parameter scenarios:
  - No deliberate consolidation: γ = 0.04 (γ_LR = 0.174).
  - Moderate consolidation: γ = 0.06.
  - Faster consolidation: γ = 0.08.
- Debt and risk premium dynamics (exact outcome for γ = 0.08):
  - Debt-to-output ratio falls from 0.52 to 0.38 by end of year five.
  - Risk premium roughly returns to steady-state level two years after consolidation begins (with γ = 0.08).
- Trade-offs:
  - Faster consolidation lowers debt and reduces risk premia more quickly.
  - Faster consolidation is more contractionary in the short- and medium-run because higher current tax rates reduce consumption, investment, and output more than under slower consolidation.
  - In the longer run (about eight years after consolidation), tax rates fall below the path with γ = 0.04, reducing negative effects later.

C. Government spending effects in different debt states (state-dependence of multipliers)
- Experiment design:
  - High-debt state simulated as in Section A with γ = 0.06 throughout.
  - Low-debt state set at stochastic steady state (debt ratio = 0.24).
  - Government consumption shocks: rise by 3.1 percent of the steady-state GDP on average for the first year (starting at t = 0).
- Conditional fiscal limit distribution under higher spending and lower initial capital:
  - Baseline mean debt-to-output ratio: 0.61.
  - Conditional mean after lower initial capital and positive government consumption shock: 0.57.
- Risk premium responses:
  - In the high-debt state, the risk premium rises by about 150 basis points at the peak after the spending shock.
  - In the low-debt state, the fiscal expansion does not increase the premium.
- Output and component responses:
  - Government consumption is expansionary only for the first year in both states.
  - Peak output multipliers are around 0.2; long-run multipliers are negative.
  - Investment and trade balance deteriorations offset expansionary effects, yielding output multipliers well below 1.
  - Output multiplier is smaller in the high-debt state mainly due to a smaller consumption multiplier; investment is less crowded out in the high-debt state because consumption responses are smaller.

### Reported multipliers and empirical outputs (exact table entries and simulation settings)
- Cumulative Multipliers of Government Consumption (Table 2) — entries presented exactly:
  - a high-debt state
    - impact 0.15 0.98 −0.86 −0.96
    - 1 year 0.09 0.86 −0.84 −0.93
    - 5 years −0.58 0.08 −1.14 −0.52
  - a low-debt state
    - impact 0.20 1.13 −0.97 −0.95
    - 1 year 0.13 1.00 −0.97 −0.89
    - 5 years −0.56 0.18 −1.30 −0.44
- Monte Carlo simulation settings and outputs:
  - Shock horizon per simulation: 1000 periods (i = 1, ...,1000).
  - Number of simulations: 10,000 (j = 1, ...,10000) to form distribution {B^{max,j}(S_t)}_{10000}.
- Decision rule convergence tolerance: 1e−7.
- Figures and labels preserved as presented (descriptive):
  - Figure 1. Estimated CDF of the baseline fiscal limit distributions for Argentina: unconditional distributions.
  - Figure 2. Estimated CDF for different revenue mobilization capacity for Argentina. Solid line—τ_max = 0.29 and θ = 0.67 (Argentina baseline); dotted-dashed line—τ_max = 0.35 and θ = 0.67; dashed line—τ_max = 0.35 and θ = 0.8.
  - Figure 3. Estimated CDF with more fluctuations in the real exchange rate. Dotted-dashed line: σ_ξ = 5.74; solid line: σ_ξ = 2.87.
  - Figure 4. Estimated CDF of large devaluation of the real exchange rate. Real depreciation induced by a large negative terms-of-trade shock in the initial state.
  - Figures 5–8. Transition dynamics of fiscal consolidation and impulse responses to government spending shocks in high- and low-debt states.

### Key policy-relevant conclusions (model-based)
- Expected future revenue capacity is a key factor explaining relatively low fiscal limits in developing countries versus developed countries.
- Fiscal limits are state-dependent: shocks that cause sharp real depreciations can suddenly increase default probabilities for economies with large external debt.
- Fiscal consolidation in a highly indebted economy:
  - Lowers debt and risk premia but imposes significant short- and medium-run output losses via higher current taxes.
  - Faster consolidation achieves faster reductions in debt and premia but is more costly in output terms in the near to medium term.
- Government spending in a high-debt state:
  - Pushes the economy closer to fiscal limits, raises risk premia and default probabilities, and yields weaker expansionary effects than in low-debt states.
- Cautionary note from model limitations:
  - The model does not incorporate negative real-world costs associated with sovereign default; if an economy is closer to fiscal limits or spending shocks are larger than simulated, multipliers could be even smaller and default risks more severe.

*Source: _wp1449 — Appendix III describes the procedure to simulate fiscal limit distributions (PDF chapter/section)*

### 1. P   arameter Calibration ............................................................................................

### 1. P   arameter Calibration ............................................................................................................27

### Introduction: scope and key empirical observations
- Sovereign debt perceived as riskier in developing than developed countries, with exceptions (recent European debt crisis).
- Examples from 2012: Belgium, United Kingdom, and the United States have net government debt-to-GDP ratios exceeding 0.8 and sovereign ratings at or above AA; Argentina and Ecuador have gross debt-to-GDP ratios at 0.48 and 0.22, respectively, but ratings of B and B− (Standard & Poor’s (2013)).
- Fiscal limits are defined as the maximum debt level a government is able and willing to service; fiscal limits are generally lower in developing countries.
- Paper uses a DSGE model with sovereign default risks to:
  - Simulate fiscal limit distributions (illustrated for Argentina).
  - Analyze fiscal policy effects under different government indebtedness states.
- Fiscal limits in the model are uncertain and forward-looking; default depends on whether current debt exceeds a realized effective fiscal limit drawn from a distribution based on economic fundamentals.
- Sovereign risk premia arise endogenously and nonlinearly as a function of government indebtedness.

### Main empirical drivers of lower fiscal limits in developing countries
- Revenue collection capacity:
  - Effective tax collection (maximum effective tax rate) and political risk play key roles in the level of fiscal limits.
  - Callen et al. (2003) estimate effective tax rate for emerging markets outside eastern Europe is only 10 percent, compared with industrial countries’ average above 30 percent.
- Real exchange rate fluctuations:
  - Increase dispersion of fiscal limit distributions via balance-sheet effects when external borrowing is substantial.
  - Currency mismatch (revenues in local currency vs. foreign-currency liabilities) raises default risk for a given debt size.
- Other noted factors (discussed in literature but not modeled here): debt intolerance, credibility, and default history.

### Model overview
- Small open, real economy with two production sectors: nontradables (N) and tradables (T).
- Key shocks included: total factor productivity (TFP), spending and tax policy, and terms of trade.
- Model solved nonlinearly by the monotone mapping method for simulations; linearized version (assuming no sovereign default) is fitted to Argentina’s post-default data from early 2000s to estimate shock processes.

### Households — preferences and decisions
- Utility:
  - Households derive utility from effective consumption (̃c_t) and leisure (1−l_t).
  - Effective consumption is a CES index of private consumption (c_t) and government consumption (g_t):
    - ̃c_t = [ω(c_t)^{(ν−1)/ν} + (1−ω)(g_t)^{(ν−1)/ν}]^{ν/(ν−1)}
    - ω is the weight of private consumption; ν > 0 is the elasticity of substitution between private and government consumption.
    - Special cases: ν = 0 (perfect complements), ν → ∞ (perfect substitutes).
- Representative household maximizes expected lifetime utility:
  - U_t = Σ_{t=0}^∞ β^t [log ̃c_t − φ l_t^{1+σ}/(1+σ)]
  - β ∈ (0,1) is the discount factor; σ is inverse of Frisch elasticity.
- Budget constraint includes income tax τ_t, transfers z, sectoral capital returns r^N_t, r^T_t, and investment with adjustment costs parameter κ.
- Capital is sector-specific with law of motion k^j_t = (1−δ)k^j_{t−1} + i^j_t.
- Private consumption and investment are CES aggregates across sectors with intra-temporal elasticity χ and home bias φ.
- Labor aggregation allows some mobility across sectors with elasticity χ_l and steady-state labor share φ_l.

### Firms — technology and prices
- Production: Cobb-Douglas for both sectors
  - y^j_t = a^j_t (k^j_{t−1})^{1−α_j} (l^j_t)^{α_j}, j ∈ {N, T}
- Sectoral TFP follows AR(1):
  - ln(a^j_t / a^j) = ρ_a ln(a^j_{t−1} / a^j) + ε^a_t, ε^a_t ∼ N(0, σ_a^2)
- Tradable sector produces only for exports; domestic tradable demand met by imports priced at s_t (real exchange rate).
- Terms of trade ξ_t ≡ p^x_t s_t follow:
  - ln(ξ_t / ξ) = ρ_ξ ln(ξ_{t−1} / ξ) + ε^ξ_t, ε^ξ_t ∼ N(0, σ_ξ^2)

### Government — budget, bonds, and fiscal rules
- Government issues external bond b*_t and collects income tax τ_t to finance government consumption g_t, transfers z, and debt service.
- Government consumption is CES of nontradables and tradables with home bias φ_G and intra-temporal elasticity χ; price p^G_t defined accordingly.
- Period flow budget constraint:
  - T_t + q_t s_t b*_t = s_t (1−∆_t) b*_{t−1} + p^G_t g_t + z
  - Where T_t ≡ τ_t (w_t l_t + r^N_t k^N_{t−1} + r^T_t k^T_{t−1}), and q_t is bond price.
- Foreign creditors are risk-neutral with demand:
  - q_t = β E_t (1 − ∆_{t+1})
- Government intertemporal budget constraint:
  - (1 − ∆_t) b*_{t−1} = Σ_{i=0}^∞ β^i E_t [ (T_{t+i} − p^G_{t+i} g_{t+i} − z) / s_{t+i} ]

### Default scheme
- Default decision depends on realized effective fiscal limit B^{max}_t drawn from distribution B^{max}(S_t) conditioned on state S_t:
  - ∆_t = 0 if b*_{t−1} < B^{max}_t; ∆_t = d if b*_{t−1} ≥ B^{max}_t
  - B^{max}_t ∼ B^{max}(S_t)
- Simulation of B^{max}(S_t) described in Section IV (not included in this excerpt).

### Fiscal policy rules and behavioral assumptions
- Government consumption responds procyclically with a one-quarter delay to output y_{t−1}.
- Tax and government consumption rules:
  - ln(τ_t / τ) = ρ_τ ln(τ_{t−1} / τ) + γ ln(b^{d*}_t / b^*) + ε^τ_t, γ > 0
  - ln(g_t / g) = ρ_g ln(g_{t−1} / g) + η_g ln(y_{t−1} / y) + ε^g_t
  - ε^τ_t, ε^g_t ∼ N(0, σ_i^2), i ∈ {τ, g}
- In the model, income taxes are the adjustment instrument to maintain debt sustainability; government consumption is assumed harder to cut in developing-country contexts.

### Aggregation and market clearing
- Aggregate output in local goods:
  - y_t = p^N_t y^N_t + ξ_t s_t y^T_t
- Nontradables market clearing condition (involving consumption, investment, government consumption, and investment adjustment costs) given in equation (20).
- Balance-of-payments condition:
  - c_t + i_t + investment adjustment cost terms + p^G_t g_t − y_t = s_t [ q_t b*_t − (1 − ∆_t) b*_{t−1} ]

### Fiscal policy and spending effects (high-level findings from model experiments)
- Fiscal consolidations:
  - Faster consolidations return risk premia to steady-state more quickly but are more contractionary (larger output reductions) than slower consolidations when implemented via income tax hikes.
  - Higher current and expected future tax rates reduce consumption, labor, and investment.
- Government spending multipliers:
  - Government consumption enters household utility as a complement to private consumption to match empirical short-run stimulative effects.
  - Fiscal multipliers are smaller when the economy is near fiscal limits (high-debt state), though the difference is moderate.
  - In a high-debt state, higher income tax rates needed to service debt reduce the after-tax wage rate and increase the economic cost of raising consumption via leisure trade-offs, making government consumption less expansionary.

*Source: _wp1449 - 1. P   arameter Calibration ............................................................................................................27*

### Appendix I lists the equilibrium conditions of the model.

### _wp1449 - Appendix I lists the equilibrium conditions of the model.

### III. ESTIMATION AND CALIBRATION — model setup and calibration
- Model frequency and solution:
  - The model is at a quarterly frequency.
  - The linearized model is solved by Sims’s (2001) method.
  - Estimation is performed on the log-linearized model assuming no default.
- Observables used in estimation:
  - Four observables: real GDP, government spending, revenues, and the real exchange rate.
- Calibration of key structural parameters:
  - Discount factor: β = 0.98.
  - Depreciation rate: δ = 0.03.
  - Tradable share in CPI for Argentina: 0.53.
  - Government consumption home-bias parameter: φ_G = 0.6.
  - Weight of private consumption in effective consumption: ω = 0.8.
  - Elasticity of substitution between private and government consumption: ν = 0.49.
  - Elasticity of substitution between tradables and nontradables in c_t and g_t (χ): 0.44.
  - Sectoral labor mobility parameter: ξ_l = 1.
  - Investment adjustment parameter: κ = 1.7.
- Default and haircut calibration:
  - Constant quarterly haircut rate: 0.07 (equivalent to 0.28 for the annual rate).
- Labor shares and labor supply:
  - Labor income share in nontradables: α_N = 0.6.
  - Labor income share in tradables: α_T = 0.55.
  - Labor disutility weight φ set such that steady-state fraction of time devoted to work = 0.2.
- Steady-state fiscal calibration (sample 2003Q1:2012Q2):
  - Government spending share of output = 0.1476.
  - Tax rate (total revenues to GDP) = 0.227.
  - Debt-to-annual output ratio (external public debt) = 0.24.

### Estimation priors and posterior-mode results
- Priors for estimated parameters:
  - AR(1) coefficients (ρ’s): beta distribution with mean 0.5 and standard deviation 0.2.
  - Standard deviations (σ’s) of all shocks: inverse gamma distribution with mean 0.1 and standard deviation of infinity.
  - Cyclical fiscal parameter η_g: normal distribution with mean 0.5 and standard deviation 0.2 (puts more weight on procyclical spending).
  - Fiscal adjustment parameter γ: gamma distribution with mean 0.05 and standard deviation 0.02; restriction γ > 0 is imposed.
- Posterior-mode estimates:
  - η_g = 0.1 (government spending is weakly procyclical).
  - γ = 0.06 (response magnitude of income tax rate to debt).

### IV. FISCAL LIMIT DISTRIBUTION — definition and simulation approach
- Definition of fiscal limit:
  - Fiscal limits are defined as the maximum level of debt in units of local goods that a government is able and willing to service.
  - In terms of ability to pay, the maximum debt level equals the sum of all future discounted maximum primary surpluses.
- Computation of period maximum primary surplus:
  - The tax rate in each period when computing maximum surplus is set to the maximum tax rate τ_max.
  - Baseline τ_max is set to 0.29.
- Political willingness to pay:
  - Willingness to pay is proxied by a political risk factor 0 < θ ≤ 1.
  - To calibrate θ, the ICRG index of political risk is used.
  - Argentina average rating in sample periods = 66.5 out of 100.
  - θ is set to 0.67 for Argentina.
- State-dependent fiscal limit expression (as modified from the intertemporal budget constraint):
  - B_max(S_i) ∼ [ sum_{i=0}^∞ β^t θ 1_{smax_{t+i}} (T^max_{t+i} − p^G_{t+i} g_{t+i} − z) ] where the superscript max indicates variables under τ_t = τ_max and S_t = {ε^a_t, ε^g_t, ε^ξ_t, k^N_{t−1}, k^T_{t−1}}.
- Simulation methodology:
  - Unconditional baseline distributions are simulated with an initial state at the steady state.
  - State-dependent distributions are simulated conditional on an initial large terms-of-trade shock.
  - For each draw of a fiscal limit B_max(S_t), simulations are conditional on the current state S_t and on particular sequences of realized shocks using Markov Chain Monte Carlo simulations.
  - Assumptions in computing B_max:
    - Government does not default in the initial period t (Δ_t = 0).
    - For analyses under an initial high-debt state, the debt-to-output ratio is chosen so that the default probability is moderate.
    - The expectation operator is dropped when computing each draw of B_max from the simulated sequences.
    - The infinite sum of maximum primary surpluses is discounted by the political risk factor θ.

*Source: _wp1449 - Appendix I lists the equilibrium conditions of the model.*

### Appendix III describes the procedure to

### _wp1449 - Appendix III describes the procedure to simulate fiscal limit distributions

### Appendix III: procedure to simulate fiscal limit distributions
- Fiscal limits are defined by B_max(S_t) ∼ [∑_{i=0}^{∞} β^{i} θ^{1} s_{max,t+i} (T_{max,t+i} − p_{G,t+i} g_{t+i} − z )] (equation (III.1)), where θ is the political risk factor and S_t = {ε^a_t, ε^g_t, ε^ξ_t, k^N_{t−1}, k^T_{t−1}} indicates the initial state.
- Simulation procedure:
  - Decision rules for non-tradable sector relative price, labor, and capital are p^N_{max,t} = m_p(S_t), l^N_{max,t} = m_l(S_t), k^N_{max,t} = m_k(S_t).
  - After convergence of m_p(.), m_l(.), m_k(.), derive T_{max,t} = m_T(S_t) and s_{max,t} = m_s(S_t) consistent with household and firm optimality conditions.

### Baseline fiscal limit distribution for Argentina (CDF properties and historical comparisons)
- Properties of the baseline CDF for Argentina:
  - Default probability is roughly zero when the debt-to-GDP ratio is below 0.45.
  - Default probability climbs to almost 1 when the debt-to-GDP ratio reaches 0.7.
- Historical external debt-to-GNP ratios at years of default:
  - 0.55 in 1982.
  - 0.53 in 2001.
- The estimated fiscal limits for Argentina cover actual debt levels in the two recent sovereign default episodes.

### B. Revenue collection capacity — sensitivity to maximum tax rate and political risk
- Baseline and alternative parameterizations:
  - Baseline: τ_max = 0.29, θ = 0.67 (solid line).
  - Alternative A: τ_max = 0.35, θ = 0.67 (dashed-solid line).
  - Alternative B: τ_max = 0.35, θ = 0.8 (dashed line).
- Impacts on mean of fiscal limit distribution:
  - Baseline mean: 0.61.
  - Raising τ_max from 0.29 to 0.35 (same θ = 0.67) increases mean to 1.02.
  - With θ = 0.8 and τ_max = 0.35, mean rises to 1.22.
- Quantitative sensitivity:
  - A one-percentage point increase in the tax rate raises the mean of fiscal limits by almost 7 percent of GDP for Argentina.
- Policy-relevant insight:
  - Strengthening revenue collection (raising τ_max) can be effective in raising fiscal limits in developing countries, whereas cutting government spending offers limited room given low government spending shares.

### C. Devaluation and balance sheet effects
- Terms-of-trade volatility experiment:
  - Baseline σ_ξ = 2.87.
  - Alternative with twice volatility σ_ξ = 5.74.
  - At debt-to-GDP ratio 0.55, default probability rises from 0.06 (baseline) to 0.25 (higher σ_ξ).
- Large devaluation (conditional distribution) experiment:
  - Subject economy to a −30-percent terms-of-trade shock → initial real depreciation of 20 percent from steady state.
  - At debt-to-GDP ratio 0.55, default probability increases from 0.06 (baseline) to about 0.4 (conditional).
- Implications:
  - Large negative terms-of-trade shocks or sudden real depreciations can substantially shift fiscal limit distributions left and raise default probabilities.
  - Other shocks (e.g., capital flow shocks) can similarly affect fiscal limits.

### V. Fiscal policy in a highly indebted economy — calibration to Argentina

A. The economy in a high-debt state (simulation setup and initial impacts)
- High-debt scenario construction:
  - Sequence of small negative TFP shocks of −1percent each period for 57 quarters starting in the steady state (t = −80).
  - Initial steady-state debt-to-annual GDP ratio = 0.24.
  - At t = 0 (start of high-debt state), debt-to-annual GDP ratio climbs to 0.52.
  - From t = −80 to −1, government sets γ = 0.04 (below estimated γ = 0.06 for Argentina).
  - At t = 0, k^N_{−1} and k^T_{−1} are about 14 and 9 percent below their steady-state values.
  - At t = 0 the interest rate increases by about 43 basis points relative to the steady-state level.
- Short-run macro impacts at t = 0 (relative to steady state):
  - Consumption: falls by 8.0 percent.
  - Investment/saving: falls by 5.6 percent.
  - Labor: increases by 1.4 percent.
  - Output: falls by 4.3 percent.

B. Fiscal consolidation (scenarios and dynamic trade-offs)
- Fiscal adjustment scenarios (γ values):
  - No deliberate consolidation: γ = 0.04 (γ_LR = 0.174).
  - Moderate consolidation: γ = 0.06.
  - Faster consolidation: γ = 0.08.
- Debt and risk premium dynamics:
  - With γ = 0.08, debt-to-output ratio falls from 0.52 to 0.38 by end of year five.
  - Risk premium roughly returns to steady-state level two years after consolidation begins (with γ = 0.08).
- Trade-offs:
  - Faster consolidation lowers debt and reduces risk premia more quickly.
  - Faster consolidation is more counterproductive in terms of short- and medium-run output losses because higher current tax rates used to retire debt reduce consumption, investment, and output more than under slower consolidation.
  - In longer run (about eight years after consolidation), tax rates fall below the path with γ = 0.04, reducing negative effects later.

C. Government spending effects in different debt states (state-dependence of multipliers)
- Experiment design:
  - High-debt state simulated as in Section A but with γ = 0.06 throughout.
  - Low-debt state set at stochastic steady state (debt ratio = 0.24).
  - Government consumption shocks: rise by 3.1 percent of the steady-state GDP on average for the first year (starting at t = 0).
- Conditional fiscal limit distribution under higher spending and lower initial capital:
  - Baseline mean debt-to-output ratio: 0.61.
  - Conditional mean after lower initial capital and positive government consumption shock: 0.57.
- Risk premium responses:
  - In the high-debt state, the risk premium rises by about 150 basis points at the peak after the spending shock.
  - In the low-debt state, the fiscal expansion does not increase the premium.
- Output and components:
  - Government consumption is expansionary only for the first year in both states.
  - Peak output multipliers are around 0.2; long-run multipliers are negative.
  - Channels:
    - Positive consumption multipliers (complementarity with government consumption) help short-run expansion.
    - Investment and trade balance deteriorations offset expansionary effects, yielding output multipliers well below 1.
    - Spending increases raise debt-to-output and, when near fiscal limits, materially raise risk premia which amplify negative effects.
  - Comparison across states:
    - Output multiplier is smaller in the high-debt state mainly due to smaller consumption multiplier.
    - Investment is less crowded out in the high-debt state because consumption responses are smaller.

### VI. Conclusion — key takeaways
- Expected future revenue capacity is a key factor explaining relatively low fiscal limits in developing countries versus developed countries.
- Fiscal limits are state-dependent: shocks that cause sharp real depreciations can suddenly increase default probabilities for economies with large external debt.
- Fiscal consolidation in a highly indebted economy:
  - Lowers debt and risk premia but imposes significant short- and medium-run output losses via higher current taxes.
  - Faster consolidation achieves faster reductions in debt and premia but is more costly in output terms in the near to medium term.
- Government spending in a high-debt state:
  - Pushes the economy closer to fiscal limits, raises risk premia and default probabilities, and yields weaker expansionary effects than in low-debt states.
- Caution: the model does not incorporate negative real-world costs associated with sovereign default; if an economy is closer to fiscal limits or spending shocks are larger than simulated, multipliers could be even smaller and default risks more severe.

*Italic: Source — _wp1449 - Appendix III describes the procedure to simulate fiscal limit distributions (PDF chapter/section)*

### 1. Define the grid points by discretizing the state space. Make initial guesses form

### _wp1449 - 1. Define the grid points by discretizing the state space. Make initial guesses form

### Solving the nonlinear model with tax rate fixed at τ_max (decision rules m_p, m_l, m_k)
- Step 1: Define the grid points by discretizing the state space. Make initial guesses for m_p0, m_l0, and m_k0 over the state space.
- Step 2: At each grid point, solve the nonlinear model assuming the tax rate is always at τ_max using given rules m_p_{i−1}, m_l_{i−1}, and m_k_{i−1}, and obtain updated rules m_p_i, m_l_i, and m_k_i:
  - (a) Derive p^G_t and s_t in terms of p^N_t using (I.20) and (I.21).
  - (b) Given l^N_t, compute y^N_t, w^N_t, and r^N_t using the optimization conditions for non-tradable sector firms, (I.14)-(I.16).
  - (c) From the labor supply in the tradable and non-tradable sectors, (I.9) and (I.10), derive
    l^T_t / l^N_t = (1−φ_l)/φ_l * (w^T_t / w^N_t)^{χ_l}. (I II.2)
    From the wage equations, (I.15) and (I.19), derive
    l^T_t = l^N_t (Γ)^{χ_l(α_N−1)χ_l−1} (III.3)
    with Γ = α_N p^N_t a^N_t (k^N_{t−1})^{1−α_N} α_T ξ_t s_t a^T_t (k^T_t)^{1−α_T} (χ_l/(1−χ_l))^{1/χ_l}. (I II.4)
    Then compute w^T_t, l^T_t, l_t using (I.8)-(I.10), and aggregate wage using
    w^{1+φ_l}_t = χ_l (w^N_t)^{1+φ_l} + (1−χ_l) (w^T_t)^{1+φ_l}. (III.5)
  - (d) Use a nonlinear solver to compute consumption c_t and the marginal utility of consumption λ_t from (I.3), combining with (I.1) and (I.2) to yield
    ω c_t + (1−ω) g^{ν−1 \over ν}_t c^{1 \over ν}_t = ω λ_t. (I II.6)
  - (e) Given k^N_t and initial state k^N_{t−1}, i^N_t is computed from (I.12). From (I.4), compute Tobin’s Q in the non-tradable sector Q^N_t.
  - (f) Given c_t, g_t, and D^N_t in (I.23), solve tradable sector variables: i^T_t from (I.22), k^T_t from (I.13), r^T_t from (I.15), and Q^T_t from (I.5).
  - (g) Use linear interpolation to obtain m_p_{i−1}(S_{t+1}), m_l_{i−1}(S_{t+1}), and m_k_{i−1}(S_{t+1}), where S_{t+1} = (ε^a_{t+1}, ε^g_{t+1}, ε^ξ_{t+1}, k^N_t, k^T_t). Then solve λ_{t+1}, i^N_{t+1}, i^T_{t+1}, Q^N_{t+1}, Q^T_{t+1}, r^N_{t+1}, and r^T_{t+1}.
  - (h) Update decision rules m_p_i, m_l_i, and m_k_i using (I.6), (I.7), and the combined equation from (I.25) and (I.27) (government debt does not appear explicitly).
- Step 3: Check convergence of the decision rules. If |m_p_i − m_p_{i−1}|, |m_l_i − m_l_{i−1}|, or |m_k_i − m_k_{i−1}| is above the desired tolerance (set to 1e−7), go back to Step 2. Otherwise, m_p_i, m_l_i, and m_k_i are the decision rules.
- Step 4: Use the converged rules—m_p, m_l, and m_k—to compute decision rules for m_T_i and m_s_i. After solving the maximum tax revenue m_T(.) and m_s(.), obtain the distribution of fiscal limits using Markov Chain Monte Carlo simulations (procedures below).

### Computing fiscal limit distributions (Monte Carlo simulation)
- For each simulation j:
  - Randomly draw exogenous shocks for TFP (ε^{a,j}_{t+i}), government consumption (ε^{g,j}_{t+i}), and terms of trade (ε^{ξ,j}_{t+i}) for 1000 periods, i = {1,2,3, ...1000}, conditional on starting state S_t = {ε^a_t, ε^g_t, ε^ξ_t, k^N_{t−1}, k^T_{t−1}}.
  - At each period obtain T^{max,j}_{t+i} and s^{max,j}_{t+i} (i = 1, ...,1000) by interpolating on decision rules m_T(.) and m_s(.).
  - Compute the fiscal limit for simulation j, conditional on S_t and selected shock sequences:
    B^{max,j}(S_t) = \sum_{i=0}^\infty β^i θ^{1 \over s^{max,j}_{t+i}} (T^{max,j}_{t+i} − p^G_{j,t+i} g_{j,t+i} − z). (III.7)
- Repeat the simulation for 10,000 times (j = {1, ...,10000}) to obtain {B^{max,j}(S_t)}_{j=1}^{10000}, forming the distribution of B^{max}(S_t).

### Solving the nonlinear model when defaults are allowed (decision rules f_b, f_p, f_l, f_k)
- State space when solving the model with defaults: S_t = {b^{d*}_t, ε^a_t, ε^g_t, k^N_{t−1}, k^T_{t−1}}. (Note: ε^ξ_t dropped in this state vector for the default analysis described.)
- Step 1: Define grid points by discretizing the state space. Make initial guesses for f_{b0}, f_{p0}, f_{l0}, and f_{k0} over the state space.
- Step 2: At each grid point, solve the nonlinear model and obtain updated rules f_{b,i}, f_{p,i}, f_{l,i}, and f_{k,i} using given rules f_{b,i−1}, f_{p,i−1}, f_{l,i−1}, and f_{k,i−1}:
  - (a) Derive τ_t in terms of b^{d*}_t using (I.28).
  - (b) Derive p^G_t and s_t in terms of p^N_t using (I.20) and (I.21).
  - (c) Given l^N_t, compute y^N_t, w^N_t, and r^N_t using (I.14)-(I.16).
  - (d) Compute l^T_t from (I.9) and (I.10) and the wage equations (I.15) and (I.19); then compute w^T_t, l^T_t, l_t using (I.8)-(I.10), and the aggregate wage.
  - (e) Use a nonlinear solver to compute consumption c_t from (I.1)-(I.3).
  - (f) Obtain i^N_t given k^N_t and k^N_{t−1} from (I.12), and compute Q^N_t from (I.4).
  - (g) Given c_t, g_t, and D^N_t in (I.23), solve tradable sector variables i^T_t from (I.22), k^T_t from (I.13), r^T_t from (I.15), and Q^T_t from (I.5).
  - (h) Use linear interpolation to obtain f_{b,i−1}(S_{t+1}), f_{p,i−1}(S_{t+1}), f_{l,i−1}(S_{t+1}), and f_{k,i−1}(S_{t+1}), where S_{t+1} = (b^{d*}_{t+1}, ε^a_{t+1}, ε^g_{t+1}, k^N_t, k^T_t). Then solve λ_{t+1}, τ_{t+1}, i^N_{t+1}, i^T_{t+1}, Q^N_{t+1}, Q^T_{t+1}, r^N_{t+1}, r^T_{t+1}, and compute q_t using (I.26).
  - (i) Update decision rules f_{b,i}, f_{p,i}, f_{l,i}, and f_{k,i} using (I.6), (I.7), (I.25), and (I.27).
- Step 3: Check convergence of the decision rules. If |f_{b,i} − f_{b,i−1}|, or |f_{p,i} − f_{p,i−1}|, or |f_{l,i} − f_{l,i−1}|, or |f_{k,i} − f_{k,i−1}| are above the desired tolerance (set to 1e−7), iterate Step 2; otherwise f_{b,i}, f_{p,i}, f_{l,i}, and f_{k,i} are the decision rules.

### Parameter calibration (exact values as listed)
- β the discount factor 0.98
- σ inverse of Frisch elasticity for labor supply 2
- δ capital depreciation rate for capital (non-tradable and tradable sectors) 0.03
- χ substitution elasticity b/w tradables and nontradables for c_t, g_t 0.44
- χ_l substitution elasticity b/w l^N_t and l^T_t for l_t 1
- φ home bias in c_t, i^N_t 0.47
- φ_l steady-state labor income share of the nontradable sector in labor income 0.5019
- φ_g home bias in g_t 0.6
- φ utility weight on leisure 40.6
- α_N labor income share of the nontradable sector 0.6
- α_T labor income share of the tradable sector 0.55
- κ investment adjustment cost (non-tradable and tradable sectors) 1.7
- ω preference weight on c_t in effective consumption 0.8
- ν elasticity of substitution b/w c_t and g_t 0.49
- τ income tax rate 0.227
- d haircut rate if default 0.07
- η_g government spending response to y_{t−1} 0.10
- γ_τ_t response to stabilize debt 0.06
- ρ_g AR(1) coefficient in g_t 0.37
- ρ_τ AR(1) coefficient in τ_t 0.77
- ρ_a AR(1) coefficient in a^N_t and a^T_t 0.82
- ρ_ξ AR(1) coefficient in ξ_t 0.76
- σ_g standard deviation of ε_g 2.32
- σ_τ standard deviation of ε_τ 9.11
- σ_a standard deviation of ε_a 1.48
- σ_ξ standard deviation of ε_ξ 2.87

### Empirical/model outputs and reported metrics (as presented)
- Cumulative Multipliers of Government Consumption (Table 2) — values reported for "a high-debt state" and "a low-debt state" (rows labeled impact, 1 year, 5 years) with entries as presented:
  - a high-debt state
    - impact 0.15 0.98 −0.86 −0.96
    - 1 year 0.09 0.86 −0.84 −0.93
    - 5 years −0.58 0.08 −1.14 −0.52
  - a low-debt state
    - impact 0.20 1.13 −0.97 −0.95
    - 1 year 0.13 1.00 −0.97 −0.89
    - 5 years −0.56 0.18 −1.30 −0.44
- Monte Carlo simulation settings and outputs:
  - Shock horizon per simulation: 1000 periods (i = 1, ...,1000).
  - Number of simulations: 10,000 (j = 1, ...,10000) to form distribution {B^{max,j}(S_t)}_{10000}.
- Figures and reported CDF comparisons (descriptive labels preserved):
  - Figure 1. Estimated CDF of the baseline fiscal limit distributions for Argentina: unconditional distributions.
  - Figure 2. Estimated CDF for different revenue mobilization capacity for Argentina. Solid line—τ_max = 0.29 and θ = 0.67 (Argentina baseline); dotted-dashed line—τ_max = 0.35 and θ = 0.67; dashed line—τ_max = 0.35 and θ = 0.8.
  - Figure 3. Estimated CDF with more fluctuations in the real exchange rate. The dotted-dashed line assumes a larger standard deviation of term-of-trade shocks σ_ξ = 5.74; the solid line has σ_ξ = 2.87.
  - Figure 4. Estimated CDF of large devaluation of the real exchange rate. Real depreciation is induced by a large negative terms-of-trade shock in the initial state.
  - Figures 5–8. Transition dynamics of fiscal consolidation and impulse responses to government spending shocks in high- and low-debt states (axes and legend labels preserved as presented).
- Decision rule convergence tolerance: 1e−7.

*Source: _wp1449 - 1. Define the grid points by discretizing the state space. Make initial guesses form (IMF working paper appendix text provided).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1449.pdf_